The bill for the ambitious redevelopment project on Rolleston Ave in central Christchurch has now risen from $205 million to an estimated $247 million.
It has also pushed the reopening of the facility out to 2029.
The museum awarded the contract for its new base-isolated basement and five-level building in mid-November to Leighs Construction.
The first two stages of the five-year redevelopment project have already been completed.
That includes the demolition of the 20th-century buildings and the above-ground strengthening of the Robert McDougall Gallery.
Museum director Anthony Wright said the work has progressed to the next stage.
"First, they'll be strengthening of the ground floor of the McDougall Gallery with a temporary support structure and piles so that the building can be separated from its existing basement.
"The old basement, which is weak and unable to take the building long term, will then be demolished and excavated out to make way for a new, much larger basement."
Museum officials say tenders submitted for the construction contract came in well above their anticipated budget, prompting them to find cost savings of about $11 million.
An unexpected $3.8 million needed to remove asbestos from the Robert McDougall Gallery has added to the cost blowouts, together with an extra $5 million blamed on unexpected ground conditions, which has slowed progress beneath the gallery.
The additional costs have increased the funding shortfall for the project to just over $86 million.
Wright said the museum currently has $160.4 million set aside for the build.
"At the moment we have enough funds in hand to substantively complete the construction of the new building, which will wrap around the heritage buildings and connect to the Robert McDougall gallery."
He said the team are actively working on a fundraising plan, and are confident of raising the extra money needed to fit out the building and exhibition spaces. All going well, the redeveloped museum is scheduled to reopen in mid-2029.
- By Geoff Sloan, made with the support of NZ On Air